Posted by Kayleigh on Wednesday, April 10, 2013 at 12:03pm.
Consider the functions
f(x)= 5x+4/x+3(This is a fraction) and
g(x)= 3x4/5x(This is a fraction)
a)Find f(g(x))
b)Find g(f(x))
c)Determine whether the functions f and g are inverses of each other.

Consider the functions  Steve, Wednesday, April 10, 2013 at 12:37pm
f(g) = (5g+4)/(g+3)
= (5(3x4)/(5x)+4) / ((3x4)/(5x)+3)
= x
g(f) = (3f4)/(5f)
= (3((5x+4)/(x+3))4) / (5((5x+4)/(x+3)))
= x
since f(g) = g(f) = x, they are inverses

Consider the functions  Kayleigh, Wednesday, April 10, 2013 at 12:44pm
What are the values that need to be excluded?

Consider the functions  Steve, Wednesday, April 10, 2013 at 12:53pm
whatever makes the denominator zero must be excluded, since division by zero is undefined.
So, for f(g), x=5 is not allowed, since g(5) is not defined. In addition, since f(3) is not defined, any x where g(x) = 3 must also be excluded. Luckily, there is no such x.
Use similar reasoning for g(f).

Consider the functions  Kayleigh, Wednesday, April 10, 2013 at 12:56pm
So there are no values to be excluded?

Consider the functions  Steve, Wednesday, April 10, 2013 at 1:04pm
Read what I said. You have to exclude x=5 because g(5) is not defined. Therefore, f(g(5)) is also not defined.
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